Database Reference
In-Depth Information
α
∗
(
Definition 50
Given a view
V
=
q
B
(
x
)
B
of a database
B
=
B
)
, a model of
the schema
B
, and an insertion request
+
t
, we say that database insertion
B
is a
translation for
B
causes the insertion of
t
into
V
when applied to
B
.More
formally, let
V
=
q
B
(
x
)
B
be the new view, obtained from the minimally updated
database
B
=
+
t
if
α
1
(
)
, where
α
1
B
∪
B
=
B
is the new updated model of
B
, and let
V
\
V
=
V
be the actual inserted view tuples (the
view insertions induced by
B
).
We say that
V
.
We denote the update of a model of
B
is a VIT for
+
t
if
t
⊆
B
induced by VIT for
+
t
over a sin-
M
Pn
⇒
gle view
V
by a transition
α
∗
====
α
1
, where
P
n
is a sequential composi-
tion of
RA
arrows in the Application Plan considered as a program of categorial
machine
M
RC
which executes the inserting of tuples in
.
From Proposition
30
in Sect.
6.2.2
, this transition corresponds to the natural trans-
formation
η
P
n
:
B
of the schema
B
α
1
DB
Sch
(G(
B
))
) such that
α
∗
(an arrow in
Int(G(
B
))
⊆
α
∗
(
α
1
(
f
I
=
)
, defined by Corollary
17
and specified in Exam-
ple
34
as an arrow in
DB
, is obtained from 'INSERT...' SQL statements used to
insert the tuples in
η
P
n
(
B
)
:
B
)
→
B
B
.
If
V
=
t
then
B
is an
exact
translation (i.e., side-effect free) for
+
t
. Other-
wise
t
.
The algorithms for translating view insertions can be, for example, used from
operations defined in [
14
].
B
is inexact, that is, with side-effects (or extra insertions)
E
=
V
\
Proposition 32
Let us consider a database mapping system
(
graph
)
G
=
(V
G
,E
G
)
with a current mapping-interpretation α
∗
:
Sch
(B)
→
DB
(
i
.
e
.,
from Definition
11
and Proposition
16
,
α
∗
∈
DB
Sch
(G)
)
which is a model of each database
schema in V
G
(
but not necessarily satisfies all inter-schema mappings in G
)
with
A
Int(G)
⊆
α
∗
(
=
A
) obtained by inserting some tuples in
A
and there exists
M
AB
={
Φ
}∈
E
G
,
where Φ is a normalized SOtgd formula
f
∀
x
1
q
A
1
(
x
1
)
r
B,
1
(
t
1
)
∧···∧∀
x
m
q
A
m
(
x
m
)
r
B,m
(
t
m
)
∃
⇒
⇒
with
M
AB
=
MakeOperads(
M
AB
)
={
v
1
·
q
A,
1
,...,v
m
·
q
A,m
,
1
r
∅
}:
A
→
B
.
Let
S
B
=
(V
i
,t
i
)
α
∂
1
(v
i
)
,t
i
=
b
α
∗
(
|
V
i
=
|
d
m
∈
α(r
i
m
)
∈
A
),m
=
1
,...,k,
=
=∅
b
=
α(q
A,i
)(
d
1
,...,
d
k
)
=
,α(v
i
)(
b
)
,
for v
i
·
q
A,i
∈
MakeOperads(
M
AB
),
O(r
q
,r
i
)
q
A,i
∈
O(r
i
1
,...,r
i
k
,r
q
),v
i
∈
,
t
i
⊆
be a nonempty set where for each element (V
i
,t
i
)
t
i
is
a subset of tuples accepted to be consecutively inserted into the view V
i
(
here just
a relation α(r
i
) of a database
∈S
B
,
1
≤
i
≤
n
=|S
B
|
and hence if t
i
=
t
i
then all transitions are exact
,
i
.
e
.,
side-effect free
),
then the concatenation of update transitions
(
in Definition
50
)
B
